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# Rounding Errors - How is this achieved? watch

1. I understand how a) and b) got 10 divided by 2 and 100 divided by 2 but I do not understand how c) d) and e) got their equations to make 0.05, 0.5 and 0.005?
2. bump
3. In a nutshell, take the last number and make it one less. Then add a .5 or just a 5 at the end if it already has a decimal.
4. (Original post by Y11_Maths)
In a nutshell, take the last number and make it one less. Then add a .5 or just a 5 at the end if it already has a decimal.
Still don't understand, so for example e) is 1.14 so you are saying take the last number and make it one less so it becomes 1.13 which is then divided by 2 to make an answer?

I need a detailed explanation
5. (Original post by anon6789)
Still don't understand, so for example e) is 1.14 so you are saying take the last number and make it one less so it becomes 1.13 which is then divided by 2 to make an answer?

I need a detailed explanation
You don’t need to divide by 2. Take 1 off the last number on 1.14 so 1.13 then add on a 5 at the end so 1.135. It’s more just common sense than needing to learn a formula
6. (Original post by Y11_Maths)
You don’t need to divide by 2. Take 1 off the last number on 1.14 so 1.13 then add on a 5 at the end so 1.135. It’s more just common sense than needing to learn a formula
So ok I'll make a new number up and see if it is correct

10.6 so take that last number by one which is 10.5 then add 5 at the end so it is 10.55 for the smallest value. For the biggest value add 1 to make 10.7 then add 5 at the end to make 10.75?
7. (Original post by anon6789)
So ok I'll make a new number up and see if it is correct

10.6 so take that last number by one which is 10.5 then add 5 at the end so it is 10.55 for the smallest value. For the biggest value add 1 to make 10.7 then add 5 at the end to make 10.75?
Your lower bound is correct but for your upper bound you just have to add either a 5 to the end if it’s a decimal or a 0.5 if it’s an integer
8. 9.2 is rounded to 1 decimal place. 9.15 rounded up gives 9.2 and 9.25 rounded down also gives 9.2. The original number given in 4 signifcant figures could be +- 0.1 (1 d.p.) / 2

99 is rounded to 2 significant figures. 98.5 rounded up gives 99 and 99.5 rounded down also gives 99. The original number given in 3 signifcant figures could be +- 0.1 (2 s.f.) / 2

1.14 is rounded to 3 signifcant figures. The original number given in 4 signifcant figures could be +- 0.01 (3 s.f.) / 2

It's really the same as with a), b) and c).
9. (Original post by Y11_Maths)
Your lower bound is correct but for your upper bound you just have to add either a 5 to the end if it’s a decimal or a 0.5 if it’s an integer
I see it would of been 10.65 not 10.75?

I make cards to remember techniques so would this be correct:

Smallest Value (Lower Bound)

1) Take 1 away from the last number
2) Add 5 at the end of the last number

Example: 195 = 195 - 1 = 194 = 194 + 0.5 = 194.5

Biggest Value (Upper Bound)

1) Add 5 at the end of the last number

Example: 95 = 95 + 0.5 = 95.5, 23.2 = 23.2 + 0.05 = 23.25

Correct?
10. (Original post by anon6789)
I see it would of been 10.65 not 10.75?

I make cards to remember techniques so would this be correct:

Smallest Value (Lower Bound)

1) Take 1 away from the last number
2) Add 5 at the end of the last number

Example: 195 = 195 - 1 = 194 = 194 + 0.5 = 194.5

Biggest Value (Upper Bound)

1) Add 5 at the end of the last number

Example: 95 = 95 + 0.5 = 95.5, 23.2 = 23.2 + 0.05 = 23.25

Correct?
Yes good job
11. (Original post by Y11_Maths)
Yes good job
Thank you Maths, I'm going Higher Tier Maths and having to go through Key Stage 3 and Foundation books because I never learnt the basics, only got 3 months to learn through KS3, Foundation and Higher Tier, will I be able to do it Maths?
12. (Original post by anon6789)
Thank you Maths, I'm going Higher Tier Maths and having to go through Key Stage 3 and Foundation books because I never learnt the basics, only got 3 months to learn through KS3, Foundation and Higher Tier, will I be able to do it Maths?
If you put your mind to it and work hard I don’t see why not
13. I can give you an example: 10.2-0.05
First: make the same decimal places for both numbers: 10.20 - 0.05 = 10.15

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Updated: February 25, 2018
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